The figure shows the volume versus temperature graph for the same mass of an ideal gas corresponding to two different pressures $P_1$ and $P_2$. Then,

State Avogadro's law (Hypothesis).

In a process,the pressure of an ideal gas varies with volume as $P = \frac{a}{1 + (V/b)^2}$,where $a$ and $b$ are constants. What is the temperature of the gas when the volume of $1$ mole of the gas is $V = b$?

$A$ long cylindrical pipe of radius $20 \,cm$ is closed at its upper end and has an airtight piston of negligible mass as shown. When a $50 \,kg$ mass is attached to the other end of the piston,it moves down by a distance $\Delta l$ before coming to equilibrium. Assuming air to be an ideal gas,$\Delta l / l$ (see figure) is close to ($g=10 \,m/s^2$,atmospheric pressure is $10^5 \,Pa$):

On which does the value of $\alpha_V$ depend for an ideal gas?

$A$ container of $10 \,L$ is filled with an ideal gas at a temperature of $27^{\circ} C$ at a pressure of $12 \,atm$. The volume of the container is reduced to $6 \,L$ and the temperature of the gas is increased by $30^{\circ} C$. What is the final pressure of the gas (in $\,atm$)?